2010 James K. Knowles Lectureand Caltech Solid Mechanics Symposium

James K. Knowles Lecture

Saturday, February 27, 2010, Beckman Institute Auditorium

The 1st annual James K. Knowles Lecture and Caltech Solid Mechanics Symposium was held on Saturday, February 27, 2010, in the Beckman Institute Auditorium. The inaugural James K. Knowles Lecture by
Rohan Abeyaratne,

The Lecture and Symposium are in memory of James K. Knowles, William J. Keenan, Jr. Professor of Applied Mechanics, Emeritus, who passed away on November 1, 2009. He is well known for his research contributions to the theory of nonlinear elasticity and the mathematical theories of materials and structures. Dr. Knowles inspired and influenced generations of students and scholars and authored over one hundred journal publications, as well as a textbook for graduate students entitled
Linear Vector Spaces and Cartesian Tensors
(Oxford University Press).

The Lecture and Symposium will be held annually and are made possible by the Division of Engineering and Applied Science and the support of family, friends and colleagues through donations to the James K. Knowles Memorial Fund.

"Variations on a Theme by Knowles"

In a seminal paper* in 1979, Knowles showed that mechanical energy can be dissipated, even
in an elastic material, if the motion of the continuum involves a propagating surface of strain discontinuity
(such as a shock wave or phase boundary). This opened the door to studying many important
questions concerning impact-induced shock waves and the kinetics of phase transitions in solids.
Recently, Knowles and I began to investigate the analogous class of problems for a discrete
system, i.e., a chain of particles connected by nonlinear springs. There are subtle differences
between the continuum and discrete problems. For example, if the discrete system leads to classical
nonlinear elasticity theory in the continuum limit, then motions of the continuum might involve strain
discontinuities and therefore be dissipative. However the discrete system of particles is conservative.
This indicates that the energy balance must behave in a subtle manner as the continuum limit is
taken. In this talk I will describe some preliminary work on the dynamics of a one-dimensional chain
of particles.

Rohan Abeyaratne
received his PhD (1979) from the California Institute
of Technology working under the guidance of Professor James K.
Knowles. Subsequently, Abeyaratne and Knowles engaged in a sustained
research collaboration from 1986–2009.
Abeyaratne is currently the Berg Professor of Mechanics at MIT and
the Director of the Singapore MIT Alliance for Research and Technology
(SMART)—a major new research center being established by MIT
in Singapore. This, MIT’s first research center outside Massachusetts,
is expected to engage over 500 faculty, postdoctoral, and doctoral researchers
when it is fully operational. Prior to this, Abeyaratne was Head
of the Department of Mechanical Engineering at MIT from 2001–2008 and its Associate Department
Head from 1996–2001.
Abeyaratne’s field of research interest is theoretical mechanics. A significant part of his work has
been focused on the dynamics of phase transitions though he has also done work on homogenization,
crack-tip singularities, and cavitation in solids. He co-authored a monograph entitled
Evolution of
Phase Transitions
with Knowles and wrote an ebook entitled
Mechanics of Elastic Solids. Volume 1:
Mathematical Preliminaries
.
Abeyaratne is a Fellow of ASME and a Fellow of the American Academy of Mechanics. He has served on the editorial board of four international journals and been on the scientific advisory boards of several universities including the Max Planck Institute for Mathematics in the Sciences and the Aerospace Engineering and Mechanics Department of the University of Minnesota. He recently completed serving a two-year term as President of the American Academy of Mechanics. Abeyaratne holds a MacVicar Fellowship—MIT’s highest award for contributions to education. Despite Knowles’ broad influence on Abeyaratne, which extends to music, nature, politics, fine wines etc., he was continually frustrated by his inability to teach Abeyaratne anything about baseball.